Generalized Uncorrelated Regression with Adaptive Graph for Unsupervised Feature Selection
Generalized Uncorrelated Regression with Adaptive Graph for Unsupervised Feature Selection
复制标题
用于无监督特征选择的具有自适应图的广义不相关回归模型
DOI：
10.1109/tnnls.2018.2868847
复制
发表时间：
2019-05-01
影响因子：
10.4
通讯作者：
Nie, Feiping
中科院分区：
文献类型：
--
作者：
Li, Xuelong;Zhang, Han;Nie, Feiping
由于高维数据中存在额外的本质特征，无监督特征选择作为分类或聚类任务的预处理一直占据着关键地位。尽管人们做了大量的努力，但现有的方法忽略了特征的冗余性，从而选择了冗余特征。在本文中，我们借助广义不相关约束，提出了一种改进的稀疏回归模型[广义不相关回归模型（GURM）]，用于寻找不相关但具有鉴别力的特征。得益于此，数据的结构被保持在Stiefel流形中，这避免了由传统的岭回归模型触发的潜在平凡解。此外，不相关约束使模型具有封闭形式的解。此外，我们还将基于最大熵原理的图正则化项引入到GURM模型（URAFS）中，从而将数据的局部几何结构嵌入到流形学习中。利用已有的广义幂迭代法，设计了一种有效的算法来实现URAFS。在八个基准数据集上进行了大量的实验，在七个国家的最先进的方法的聚类任务，以验证所提出的方法的有效性和优越性。
Unsupervised feature selection always occupies a key position as a preprocessing in the tasks of classification or clustering due to the existence of extra essential features within high-dimensional data. Although lots of efforts have been made, the existing methods neglect to consider the redundancy of features, and thus select redundant features. In this brief, by virtue of a generalized uncorrelated constraint, we present an improved sparse regression model [generalized uncorrelated regression model (GURM)] for seeking the uncorrelated yet discriminative features. Benefited from this, the structure of data is kept in the Stiefel manifold, which avoids the potential trivial solution triggered by a conventional ridge regression model. Besides that, the uncorrelated constraint equips the model with the closed-form solution. In addition, we also incorporate a graph regularization term based on the principle of maximum entropy into the GURM model (URAFS), so as to embed the local geometric structure of data into the manifold learning. An efficient algorithm is designed to perform URAFS by virtue of the existing generalized powered iteration method. Extensive experiments on eight benchmark data sets among seven state-of-the-art methods on the task of clustering are conducted to verify the effectiveness and superiority of the proposed method.